ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 63,   2   (1994)
pp.   193-206

ADJOINTS OF SOLUTION SEMIGROUPS AND IDENTIFIABILITY OF DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES
M. MASTINSEK

Abstract.  The paper deals with semigroups of operators associated with delay differential equation: \dot x(t)= Ax(t)+L_1 x(t-h)+L_2 x_t, where $A$ is the infinitesimal generator of an analytic semigroup on a Hilbert space $X$ and $L_1$, $L_2$ are densely defined closed operators in $X$ and $L^2(-h, 0; X)$ respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigenspaces of the generator of the adjoint semigroup are studied and the identifiability of parameters of the equation is given.

AMS subject classification.  34G10, 34K30, 47D03
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